On the other hand, since \(\mathop {\hbox{dim}}\nolimits \mathfrak {p}=64\)  is even, the Clifford algebra \(C(\mathfrak {p})\)  has a unique irreducible module, namely, the spin module \(S_G\) . By Lemma 6.9 of [1]}, we have that
\(S_G=\bigoplus _{j=0}^{62} E_{\rho _n^{(j)}}\) 
